Scenario 9.7
You are the operations manager of a firm that uses the continuous-review inventory control system.Suppose the firm operates 52 weeks a year,365 days,and has the following characteristics for its primary item:
Demand = 25,000 units/year
Ordering cost = $30/order
Holding cost = $8/unit/year
Lead time = 2 weeks
Standard deviation in weekly demand = 100 units
A normal distribution table is appended to this exam.
-Use the information in Scenario 9.7.How many orders per year does the company place if they order the economic order quantity each time?
A)less than or equal to 70 units
B)greater than 70 but less than or equal to 80 units
C)greater than 80 but less than or equal to 90 units
D)greater than 90 units

Question

Quizplus · Accepted Answer

To determine the economic order quantity, we can use the formula:
EOQ = sqrt((2SD*Annual Demand)/Holding Cost)

Plugging in the values given in the problem, we get:
EOQ = sqrt((2*100*25000)/8) = 1118.03

Since lead time is given as 2 weeks, we need to also calculate the safety stock:
Safety Stock = Z*sqrt(Lead Time*SD^2)
where Z value can be found using the standard normal distribution table for a desired service level. Let's assume a service level of 95%, which corresponds to a Z value of 1.645.

Plugging in the values, we get:
Safety Stock = 1.645*sqrt(2*100^2) = 460.83

Therefore, the reorder point is EOQ+Safety Stock = 1578.86 units.

Now, to calculate the number of orders per year, we need to divide the annual demand by the economic order quantity:
Number of Orders = Annual Demand / EOQ = 25000 / 1118.03 = 22.38

Rounding down, the company would place 22 orders per year if they order the economic order quantity each time. This corresponds to ordering 1118 units per order on average.

Since the EOQ is 1118.03, which is less than or equal to 70 units, the answer is A) less than or equal to 70 units.

Scenario 9.7 You Are the Operations Manager of a Firm That Uses